The nontrivial ground state topology in the coexistence phase of chiral d-wave superconductivity and 120-degree magnetic order on a triangular lattice

Abstract

The Z2 topological invariant is defined in the chiral d-wave superconductor having a triangular lattice in the presence of the 120-degree magnetic ordering. Analyzing the Z2 invariant, we determine the conditions of implementing topological phases in the model with regard to superconducting pairings between the nearest and next nearest neighbors. It is often supposed in such a system that the pairing parameter between the nearest neighbors should be equal to zero due to the intersite Coulomb interaction. We show that taking into account even weak pairings in the first coordination sphere leads to the disappearance of the gapless excitations of the bulk spectrum in the wide region of the parameter space. Thus, topological invariants can be defined in this region. In solving the problem of open edges it is shown that the zero energy modes are realized basically in the topologically nontrivial phases. Such zero modes are topologically protected Majorana modes. A connection between the Z2 invariant and the integer topological invariant of the ground state of the 2D lattice is established in the presence of the electron–hole symmetry and noncollinear magnetic ordering.